My first thought is no, but here's why I ask:
I had to get aquarium salt to treat my betta's fin rot and inflamed gill, and once I was at the store it took me ages to find it. I finally see a shelf with different salts on it. I knew that coral salt was not what I needed, and I didn't need marine salt either (looking back I realize that marine salt and sea salt are likely the same thing, but I was in a hurry and salt has always come from the ocean right?). I grabbed a small box labeled 'Instant Ocean Sea Salt" by Instant Ocean.
So I get home and put 1 tsp of the salt in a gallon of water that I had sitting out at room temp, and last night I put him into it. However, I read somewhere this morning that marine salt is bad for bettas, since it usually has additional chemicals in it. In a panic, I scoured my box, but there is no list of ingredients anywhere. I checked on my fish, and he was fine. In fact, better than yesterday. His gill looks a lot better and his fins aren't as bloody.
So as of now, it's been somewhere between 14-16 hrs since I put him into his salty water. He's not going to start having problems, is he? I read some horror stories about marine salt giving bettas burns.

Nothing on the box says anything about caking or added chemicals, so I think it's safe. I've been adding a teeny bit less than 1 tsp/gal anyway, just to be sure.
On the plus side, his colors have been getting better. I dunno why, but I'm not complaining. :P